Question

A man buys a house for $350,000. He makes a $150,000 down payment and amortizes the rest of the purchase price with semiannual payments over the next 13 years. The interest rate on the debt is 9%, compounded semiannually.

(a) Find the size of each payment.  the answer is not 13204.483

(b) Find the total amount paid for the purchase. the answer is not 493304

(c) Find the total interest paid over the life of the loan. the answer is not 143303

Answer 1

The quantum of the loan is $ 350000- $ 150000 = $ 200000.

The formula used to calculate the fixed monthly payment (P) required to fully amortize a loan of $ L over a term of n months at a monthly interest rate of r is

P = L[r(1 + r)ⁿ]/[(1 + r)ⁿ - 1].

Here, L = 200000, r = 9/200 = 1-045and n = 2*13 = 26

Therefore, P = 200000*(9/200)*[ (1.045)²⁶]/[ (1.045)²⁶ -1] = 9000*3.140679007/2.140679007 = $ 13204.27 ( on rounding off to the nearest cent).

(a). The size of each payment is $ 13204.27.

(b). The total amount paid for the purchase is $ 150000+ 26 *$ 13204.27 =$ 150000+ $ 343311.02= $ 493011.02.

( c). The total interest paid over the life of the loan is $ 343311.02- $ 200000 = $ 143311.02.